20*19*18*17*16 = 1860480 ways.
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There are 5040 ways.
7
27!
19*18*17*16*15 = 1,395,360
For the first spot, you can choose any one of 5 students. For the second spot, you can choose any one of the remaining 4 students. For the third spot, you can choose any one of the remaining 3 students. etc. So the answer is: 5x4x3x2x1 = 120